This season the three teams promoted to the Premiership – Brighton, Huddersfield and Newcastle – are doing better than expected; none of them are currently involved in a relegation battle, and at this point in the season with 29 games played, they are lying 10th, 15th and 16th respectively. Conversely, the teams relegated to the Championship are performing quite poorly. Sunderland are propping up the table, Hull are hovering just above the relegation zone, and only Middlesbrough are competing effectively, one place below the play-off positions.
It is interesting to speculate about the quality gap between the Premiership and the Championship; clearly there is some degree of overlap. In this post, I estimate the gap based on matches played in the 2016-17 season. The reason we can do this is because some Premiership and Championship teams met in the FA and League cup competitions; in the 2016-2017 season, there were 32 match-ups between a Premier League and Champions League team. This enables us to assess their relative strengths, and because they also compete in their own competitions we can create an overall table covering both leagues.
I used the method described by Alan Lee in “Anthology of Statistics in Sports” This starts with assuming a Poisson distribution for Goals Scored:
X is the number of goals scored, and is the mean of its distribution, which we assume depends on:
- Attacking strength of target team
- Defensive strength of opposition
- Venue (Home, Away, Neutral)
We then model the log of (ie log of the mean number of goals scored) as a linear combination of these factors, including a constant to represent the average no. of goals scored in all games.
If S.attack and S.defence are the attacking and defensive strengths respectively, the basic model is:
log(home) = const + S.attackhome – S.defenceaway + Venuehome
log(away) = const + S.attackaway – S.defencehome + Venueaway
The home and away scores for each team are assumed to be drawn from poisson distributions with a mean of home and away respectively.
To estimate the model parameters I used a Bayesian approach. Gamma priors were specified for the team strength and venue parameters.
Comparing the Premier League and the Championship.
Having estimated the team strength parameters, we can compute the goals for and against in any match. In particular we can compute the result for any team playing against a “standard opponent”. The standard opponent I chose was the average Premier League team, i.e. a hypothetical team who has an attacking strength and a defensive strength equal to the respective league averages. (Such a team would be roughly as strong as Leicester (2016/17) in attack and West Brom. (2016/17) in defence.)
To compare the strengths of the Championship and the Premiership we compare the performances of a representative team for each competition. The representative teams are hypothetical teams which have the average attacking and defensive strengths for their respective competitions. The relative strengths of the competitions is estimated from the performance of the representative Premier League team and the representative Championship team, playing away against the standard opponent. The results are shown in Table 1.
Table 1. Strengths of Average Premiership and Championship Teams
|Home Team||Opponents||Goals scored by Home team||Goals conceded by Home team|
|Average Premiership team||Average Premiership team||1.43||0.86|
|Average Premiership team||Average Championship team||2.03||0.60|
The results show that scoring 2.03 goals against Championship opponents is equivalent to scoring 1.43 goals against Premiership opponents. This means that 10 goals scored in the Championship are equivalent to 7 goals scored in the Premiership. As this 10:7 ratio depends only on the defensive strengths in the respective leagues, we could apply it to strikers as well as teams. We would expect a striker who scores 10 goals against Championship defences to score only 7 in the Premiership. This could be a useful rule of thumb in recruitment, but at the moment it isn’t clear how much the expected ratio might change from season to season.
We can also estimate the strengths of individual teams. To express this as a single number, the measure of strength is the goal difference when playing at home against the standard opponent. The results are shown in the Figure 1; the dotted line is the boundary between the first twenty teams and the rest. In theory, teams above this line belong to the Premiership.
Figure 1. Team strengths 2016-17
The table is headed by Tottenham, rather than the champions Chelsea. While the strengths are strongly correlated with the league finishing positions in 2016, some differences are to be expected. First, the results in Figure 1 are based on goals scored and conceded while league positions are based on points earned from wins and draws. Spurs’ goal difference in 2016 was 60, while Chelsea’s was only 52. Another possible reason for the differences is that the rankings in Figure 1 take some Cup matches are into account.
It is interesting to see that four Championship teams appear in the first 20 positions, indicating they are Premiership strength teams. Two of these clubs won promotion in 2016. Newcastle and Brighton in particular were expected to perform as well as other mid-table Premiership sides. Brighton, with 29 games played are in 10th, two places higher than predicted. But Newcastle’s strength seems to be overestimated more; few would argue they deserved to be rated 8th and they are currently 16th. The real surprise packet however is Huddersfield, who won promotion despite being ranked 31st in the overall table and are currently ranked 15th surpassing their 2016 form by some margin. On present evidence, there is a fair degree of noise in the predictions for individual teams, and the 2016 strength estimates for Championship sides don’t predict the 2017 season particularly well. But more seasons need to be examined to get a clearer picture.
At the other end of the table, four Premiership teams failed to make the top twenty. The three weakest, Middlesbrough (24) Hull (26), Sunderland (35) were relegated in 2016, while Watford (22) survived. Sunderland’s weakness in 2016 is reflected in their disastrous 2017 form; they are currently leading candidates for relegation from the Championship.
There are some limitations to be borne in mind.
First, the bridge between the Premiership and The Championship (and hence the estimate of their relative strengths) is based on the results of only 32 Cup matches. This is a smallish number, and adds some uncertainty to the cross-league estimates.
Secondly, the teams fielded for Cup matches are not always reflective of the real strengths of the clubs. Premiership sides sometimes field weakened teams against Championship sides to give younger or newer players some experience, or to protect their league campaign, believing that they still have a chance of winning the tie. On the other hand, Championship sides playing against Premiership sides often raise their game and put in exceptional effort, due to the psychological importance of the occasion. Together, these factors would tend to produce an underestimate of the gap between the two Leagues; the Championship might be rated rather higher than it otherwise should be.
Nevertheless, it is quite useful to have a ball-park figure to work with when recruiting from the lower league.